Can I move a backlog item between Kanban boards?

Yes, you can move backlog items between Kanban boards without any problems, by right-clicking on the backlog item and selecting "Assign to Kanban board...".

If work has started on a backlog item, make sure that the target board has columns that match the status of the backlog item and its tasks, otherwise you won't be able to assign the backlog item to that board.